Federated Learning with Manifold Regularization and Normalized Update Reaggregation

Federated Learning (FL) is an emerging collaborative machine learning framework where multiple clients train the global model without sharing their own datasets. In FL, the model inconsistency caused by the local data heterogeneity across clients results in the near-orthogonality of client updates, which leads to the global update norm reduction and slows down the convergence. Most previous works focus on eliminating the difference of parameters (or gradients) between the local and global models, which may fail to reflect the model inconsistency due to the complex structure of the machine learning model and the Euclidean space's limitation in meaningful geometric representations. In this paper, we propose FedMRUR by adopting the manifold model fusion scheme and a new global optimizer to alleviate the negative impacts. Concretely, FedMRUR adopts a hyperbolic graph manifold regularizer enforcing the representations of the data in the local and global models are close to each other in a low-dimensional subspace. Because the machine learning model has the graph structure, the distance in hyperbolic space can reflect the model bias better than the Euclidean distance. In this way, FedMRUR exploits the manifold structures of the representations to significantly reduce the model inconsistency. FedMRUR also aggregates the client updates norms as the global update norm, which can appropriately enlarge each client's contribution to the global update, thereby mitigating the norm reduction introduced by the near-orthogonality of client updates. Furthermore, we theoretically prove that our algorithm can achieve a linear speedup property for non-convex setting under partial client participation.Experiments demonstrate that FedMRUR can achieve a new state-of-the-art (SOTA) accuracy with less communication.

Stability and Generalization of the Decentralized Stochastic Gradient Descent Ascent Algorithm

The growing size of available data has attracted increasing interest in solving minimax problems in a decentralized manner for various machine learning tasks. Previous theoretical research has primarily focused on the convergence rate and communication complexity of decentralized minimax algorithms, with little attention given to their generalization. In this paper, we investigate the primal-dual generalization bound of the decentralized stochastic gradient descent ascent (D-SGDA) algorithm using the approach of algorithmic stability under both convex-concave and nonconvex-nonconcave settings. Our theory refines the algorithmic stability in a decentralized manner and demonstrates that the decentralized structure does not destroy the stability and generalization of D-SGDA, implying that it can generalize as well as the vanilla SGDA in certain situations. Our results analyze the impact of different topologies on the generalization bound of the D-SGDA algorithm beyond trivial factors such as sample sizes, learning rates, and iterations. We also evaluate the optimization error and balance it with the generalization gap to obtain the optimal population risk of D-SGDA in the convex-concave setting. Additionally, we perform several numerical experiments which validate our theoretical findings.

Modeling Path Importance for Effective Alzheimer's Disease Drug Repurposing

Recently, drug repurposing has emerged as an effective and resource-efficient paradigm for AD drug discovery. Among various methods for drug repurposing, network-based methods have shown promising results as they are capable of leveraging complex networks that integrate multiple interaction types, such as protein-protein interactions, to more effectively identify candidate drugs. However, existing approaches typically assume paths of the same length in the network have equal importance in identifying the therapeutic effect of drugs. Other domains have found that same length paths do not necessarily have the same importance. Thus, relying on this assumption may be deleterious to drug repurposing attempts. In this work, we propose MPI (Modeling Path Importance), a novel network-based method for AD drug repurposing. MPI is unique in that it prioritizes important paths via learned node embeddings, which can effectively capture a network's rich structural information. Thus, leveraging learned embeddings allows MPI to effectively differentiate the importance among paths. We evaluate MPI against a commonly used baseline method that identifies anti-AD drug candidates primarily based on the shortest paths between drugs and AD in the network. We observe that among the top-50 ranked drugs, MPI prioritizes 20.0% more drugs with anti-AD evidence compared to the baseline. Finally, Cox proportional-hazard models produced from insurance claims data aid us in identifying the use of etodolac, nicotine, and BBB-crossing ACE-INHs as having a reduced risk of AD, suggesting such drugs may be viable candidates for repurposing and should be explored further in future studies.

FlatMatch: Bridging Labeled Data and Unlabeled Data with Cross-Sharpness for Semi-Supervised Learning

Semi-Supervised Learning (SSL) has been an effective way to leverage abundant unlabeled data with extremely scarce labeled data. However, most SSL methods are commonly based on instance-wise consistency between different data transformations. Therefore, the label guidance on labeled data is hard to be propagated to unlabeled data. Consequently, the learning process on labeled data is much faster than on unlabeled data which is likely to fall into a local minima that does not favor unlabeled data, leading to sub-optimal generalization performance. In this paper, we propose FlatMatch which minimizes a cross-sharpness measure to ensure consistent learning performance between the two datasets. Specifically, we increase the empirical risk on labeled data to obtain a worst-case model which is a failure case that needs to be enhanced. Then, by leveraging the richness of unlabeled data, we penalize the prediction difference (i.e., cross-sharpness) between the worst-case model and the original model so that the learning direction is beneficial to generalization on unlabeled data. Therefore, we can calibrate the learning process without being limited to insufficient label information. As a result, the mismatched learning performance can be mitigated, further enabling the effective exploitation of unlabeled data and improving SSL performance. Through comprehensive validation, we show FlatMatch achieves state-of-the-art results in many SSL settings.

Winning Prize Comes from Losing Tickets: Improve Invariant Learning by Exploring Variant Parameters for Out-of-Distribution Generalization

Out-of-Distribution (OOD) Generalization aims to learn robust models that generalize well to various environments without fitting to distribution-specific features. Recent studies based on Lottery Ticket Hypothesis (LTH) address this problem by minimizing the learning target to find some of the parameters that are critical to the task. However, in OOD problems, such solutions are suboptimal as the learning task contains severe distribution noises, which can mislead the optimization process. Therefore, apart from finding the task-related parameters (i.e., invariant parameters), we propose Exploring Variant parameters for Invariant Learning (EVIL) which also leverages the distribution knowledge to find the parameters that are sensitive to distribution shift (i.e., variant parameters). Once the variant parameters are left out of invariant learning, a robust subnetwork that is resistant to distribution shift can be found. Additionally, the parameters that are relatively stable across distributions can be considered invariant ones to improve invariant learning. By fully exploring both variant and invariant parameters, our EVIL can effectively identify a robust subnetwork to improve OOD generalization. In extensive experiments on integrated testbed: DomainBed, EVIL can effectively and efficiently enhance many popular methods, such as ERM, IRM, SAM, etc.

Rethinking SIGN Training: Provable Nonconvex Acceleration without First- and Second-Order Gradient Lipschitz

Sign-based stochastic methods have gained attention due to their ability to achieve robust performance despite using only the sign information for parameter updates. However, the current convergence analysis of sign-based methods relies on the strong assumptions of first-order gradient Lipschitz and second-order gradient Lipschitz, which may not hold in practical tasks like deep neural network training that involve high non-smoothness. In this paper, we revisit sign-based methods and analyze their convergence under more realistic assumptions of first- and second-order smoothness. We first establish the convergence of the sign-based method under weak first-order Lipschitz. Motivated by the weak first-order Lipschitz, we propose a relaxed second-order condition that still allows for nonconvex acceleration in sign-based methods. Based on our theoretical results, we gain insights into the computational advantages of the recently developed LION algorithm. In distributed settings, we prove that this nonconvex acceleration persists with linear speedup in the number of nodes, when utilizing fast communication compression gossip protocols. The novelty of our theoretical results lies in that they are derived under much weaker assumptions, thereby expanding the provable applicability of sign-based algorithms to a wider range of problems.

Merging Experts into One: Improving Computational Efficiency of Mixture of Experts

Scaling the size of language models usually leads to remarkable advancements in NLP tasks. But it often comes with a price of growing computational cost. Although a sparse Mixture of Experts (MoE) can reduce the cost by activating a small subset of parameters (e.g., one expert) for each input, its computation escalates significantly if increasing the number of activated experts, limiting its practical utility. Can we retain the advantages of adding more experts without substantially increasing the computational costs? In this paper, we first demonstrate the superiority of selecting multiple experts and then propose a computation-efficient approach called \textbf{\texttt{Merging Experts into One}} (MEO), which reduces the computation cost to that of a single expert. Extensive experiments show that MEO significantly improves computational efficiency, e.g., FLOPS drops from 72.0G of vanilla MoE to 28.6G (MEO). Moreover, we propose a token-level attention block that further enhances the efficiency and performance of token-level MEO, e.g., 83.3\% (MEO) vs. 82.6\% (vanilla MoE) average score on the GLUE benchmark. Our code will be released upon acceptance. Code will be released at: \url{https://github.com/Shwai-He/MEO}.

Zero-Shot Sharpness-Aware Quantization for Pre-trained Language Models

Quantization is a promising approach for reducing memory overhead and accelerating inference, especially in large pre-trained language model (PLM) scenarios. While having no access to original training data due to security and privacy concerns has emerged the demand for zero-shot quantization. Most of the cutting-edge zero-shot quantization methods primarily 1) apply to computer vision tasks, and 2) neglect of overfitting problem in the generative adversarial learning process, leading to sub-optimal performance. Motivated by this, we propose a novel zero-shot sharpness-aware quantization (ZSAQ) framework for the zero-shot quantization of various PLMs. The key algorithm in solving ZSAQ is the SAM-SGA optimization, which aims to improve the quantization accuracy and model generalization via optimizing a minimax problem. We theoretically prove the convergence rate for the minimax optimization problem and this result can be applied to other nonconvex-PL minimax optimization frameworks. Extensive experiments on 11 tasks demonstrate that our method brings consistent and significant performance gains on both discriminative and generative PLMs, i.e., up to +6.98 average score. Furthermore, we empirically validate that our method can effectively improve the model generalization.

ChatGPT for Computational Topology

ChatGPT represents a significant milestone in the field of artificial intelligence (AI), finding widespread applications across diverse domains. However, its effectiveness in mathematical contexts has been somewhat constrained by its susceptibility to conceptual errors. Concurrently, topological data analysis (TDA), a relatively new discipline, has garnered substantial interest in recent years. Nonetheless, the advancement of TDA is impeded by the limited understanding of computational algorithms and coding proficiency among theoreticians. This work endeavors to bridge the gap between theoretical topological concepts and their practical implementation in computational topology through the utilization of ChatGPT. We showcase how a pure theoretician, devoid of computational experience and coding skills, can effectively transform mathematical formulations and concepts into functional code for computational topology with the assistance of ChatGPT. Our strategy outlines a productive process wherein a mathematician trains ChatGPT on pure mathematical concepts, steers ChatGPT towards generating computational topology code, and subsequently validates the generated code using established examples. Our specific case studies encompass the computation of Betti numbers, Laplacian matrices, and Dirac matrices for simplicial complexes, as well as the persistence of various homologies and Laplacians. Furthermore, we explore the application of ChatGPT in computing recently developed topological theories for hypergraphs and digraphs. This work serves as an initial step towards effectively transforming pure mathematical theories into practical computational tools, with the ultimate goal of enabling real applications across diverse fields.